| Safe Haskell | Safe |
|---|---|
| Language | Haskell98 |
Numeric.Algebra.Idempotent
Contents
- class Multiplicative r => Band r
- pow1pBand :: r -> Natural -> r
- powBand :: Unital r => r -> Natural -> r
- class Algebra r a => IdempotentAlgebra r a
- class Coalgebra r c => IdempotentCoalgebra r c
- class (Bialgebra r h, IdempotentAlgebra r h, IdempotentCoalgebra r h) => IdempotentBialgebra r h
Documentation
class Multiplicative r => Band r #
An multiplicative semigroup with idempotent multiplication.
a * a = a
Instances
| Band Bool # | |
| Band () # | |
| Band r => Band (Opposite r) # | |
| Idempotent r => Band (Exp r) # | |
| (Band a, Band b) => Band (a, b) # | |
| Band (Rect i j) # | |
| (Idempotent r, IdempotentCoalgebra r a) => Band (Covector r a) # | |
| (Band a, Band b, Band c) => Band (a, b, c) # | |
| (Band a, Band b, Band c, Band d) => Band (a, b, c, d) # | |
| (Band a, Band b, Band c, Band d, Band e) => Band (a, b, c, d, e) # | |
Idempotent algebras
class Algebra r a => IdempotentAlgebra r a #
Instances
| (Semiring r, Band r) => IdempotentAlgebra r () # | |
| (Semiring r, Band r) => IdempotentAlgebra r IntSet # | |
| (Semiring r, Band r, Ord a) => IdempotentAlgebra r (Set a) # | |
| (IdempotentAlgebra r a, IdempotentAlgebra r b) => IdempotentAlgebra r (a, b) # | |
| (IdempotentAlgebra r a, IdempotentAlgebra r b, IdempotentAlgebra r c) => IdempotentAlgebra r (a, b, c) # | |
| (IdempotentAlgebra r a, IdempotentAlgebra r b, IdempotentAlgebra r c, IdempotentAlgebra r d) => IdempotentAlgebra r (a, b, c, d) # | |
| (IdempotentAlgebra r a, IdempotentAlgebra r b, IdempotentAlgebra r c, IdempotentAlgebra r d, IdempotentAlgebra r e) => IdempotentAlgebra r (a, b, c, d, e) # | |
class Coalgebra r c => IdempotentCoalgebra r c #
Instances
| (Semiring r, Band r) => IdempotentCoalgebra r () # | |
| (Semiring r, Band r) => IdempotentCoalgebra r IntSet # | |
| (Semiring r, Band r, Ord c) => IdempotentCoalgebra r (Set c) # | |
| (IdempotentCoalgebra r a, IdempotentCoalgebra r b) => IdempotentCoalgebra r (a, b) # | |
| (IdempotentCoalgebra r a, IdempotentCoalgebra r b, IdempotentCoalgebra r c) => IdempotentCoalgebra r (a, b, c) # | |
| (IdempotentCoalgebra r a, IdempotentCoalgebra r b, IdempotentCoalgebra r c, IdempotentCoalgebra r d) => IdempotentCoalgebra r (a, b, c, d) # | |
| (IdempotentCoalgebra r a, IdempotentCoalgebra r b, IdempotentCoalgebra r c, IdempotentCoalgebra r d, IdempotentCoalgebra r e) => IdempotentCoalgebra r (a, b, c, d, e) # | |
class (Bialgebra r h, IdempotentAlgebra r h, IdempotentCoalgebra r h) => IdempotentBialgebra r h #
Instances
| (Bialgebra r h, IdempotentAlgebra r h, IdempotentCoalgebra r h) => IdempotentBialgebra r h # | |